Please help me with this pleaseee

Please Help Me With This Pleaseee

Answers

Answer 1

Answer:

x = 88.2

Step-by-step explanation:

The angle at the top of the triangle = 90° - 10° = 80°

and the left side of the triangle is x ( opposite sides of a rectangle )

Using the tangent ratio in the right triangle

tan80° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{500}{x}[/tex]

Multiply both sides by x

x × tan80° = 500 ( divide both sides by tan80° )

x = [tex]\frac{500}{tan80}[/tex] ≈ 88.2


Related Questions

The stilts increase a persons heart by 1.5 yards.If Bonnie who is 5 feet and 7 inches tall walks on stilts how tall will be.

Answers

Bonnie will be 10 feet and 1inch. Because 1.5 yards is actually 4.5 feet, since 3 feet make up 1 yard. 5 feet + 4 feet= 9 feet. 7 inches plus 6 inches(which is half a foot) = 13 inches or 1 foot and 1inch. 9 feet + 1 foot and 1 inch = 10 feet and 1 inch.

Answer:

[tex]\boxed{\text{10 ft 1 in}}[/tex]

Step-by-step explanation:

1. Convert the height of stilts to inches

1.5 yd × (36 in/1 yd) = 54 in

2. Convert Bonnie's height to inches

5ft 7in = 5 ft × (12 in/1 ft) + 7 in = 60 in + 7 in = 67 in

3. Calculate Bonnie's height on stilts

67 in + 54 in = 121 in

4. Convert inches back to feet and inches

121 in × (1 ft/12 in) = 10R1 ft = 10 ft 1 in  

Bonnie will be [tex]\boxed{\text{10 ft 1 in}}[/tex] tall on stilts.

Am I right? Can Somebody Plz Check This For Me
The following image is a visual description of which of the STEM discoveries provided in this lesson?

C is my answer

A.) black hole
B.) Blissymbol
C.) Pythagorean theorem
D.) Theory of evolution

Answers

Answer:

answer is C

Step-by-step explanation:

Answer:

Definitely C.) Pythagorean Theorem

Step-by-step explanation:

What is the solution to the system graphed below?

A) (1, 1)
B) (1, -1)
C) (-1, 1)
D) (-1, -1)

Answers

The answer is D: (-1,-1).

The solution to the system graphed below is (-1,-1) which is option D.

What is a graph?

It is a collection of various points and it is used to draw lines of different functions or equations by finding out two points and by joining them.

How to identify points on the graph?

We have to check solution of the system graphed in the question. There are two lines graphed. Both are intersecting each other at one point. A solution of a line exists at a point where they are intersecting. If we try to find the point then we need to identify origin first and then according to x and y axis points will be found. The required points will be (-1,-1).

Hence the solution of graphed system is (-1,-1).

Learn more about graphs at  https://brainly.com/question/4025726

#SPJ2

What can you say about the end behavior of the function [tex]f(x) = log_{10} (5x-1)[/tex]?

A. One end decreased and one end approaches a constant
B. One end increase and one end decreases
C. Both ends increase
D. Both ends decrease

Answers

Final answer:

For the given logarithmic function, it is undefined as x approaches negative infinity, and increases without bound as x approaches positive infinity. The correct answer is B. One end increases and one end decreases.

Explanation:

The function [tex]f(x) = log_{10} (5x-1)[/tex] is a logarithmic function with a base of 10. Its end behavior is determined by the properties of logarithmic functions.

Logarithmic functions have one side that increases without bound (to positive infinity) and one side that approaches a certain limit, but never reaches it, hence getting infinitely close to it. In this case, as x approaches negative infinity, the function becomes undefined as (5x-1) becomes a negative number and logarithm is undefined for negative values. On the other end, as x approaches positive infinity, the function will also approach positive infinity because the log of a large number gets larger.

Thus, the correct answer would be B. One end increases and one end decreases (becomes undefined).

Learn more about End Behavior of Logarithmic Function here:

https://brainly.com/question/30284289

#SPJ12

Final answer:

The end behavior of the function is that A. one end decreases and one end approaches a constant.

Explanation:

The given function is f(x) = log10 (5x-1).

To determine the end behavior of the function, we can consider the limit of the function as x approaches positive and negative infinity.

As x approaches positive infinity, the argument of the logarithm, 5x-1, will become larger and larger, resulting in a logarithm that approaches positive infinity. Therefore, the right end of the graph increases.

Similarly, as x approaches negative infinity, the argument of the logarithm will become smaller and smaller, resulting in a logarithm that approaches negative infinity. Therefore, the left end of the graph decreases.

Thus, the correct answer is A. One end decreases and one end approaches a constant.

Learn more about End behavior of a function here:

https://brainly.com/question/32061836

#SPJ12

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth. 117.8 cubic units 141.3 cubic units 235.5 cubic units 282.6 cubic units

Answers

The volume of an oblique cone, to the nearest tenth is: 235.5 cubic units.

What is the Volume of an Oblique Cone?

Volume of an oblique cone = (1/3) × π × r² × h, where r is radius and h is height of the oblique cone.

Given:

Radius = 5Height = 9π ≈ 3.14

Thus:

Volume of an oblique cone = (1/3) × 3.14 × 5² × 9

Volume of an oblique cone = 235.5 cubic units.

Learn more about volume of oblique cone on:

https://brainly.com/question/26524753

The approximate volume of the oblique cone is V = 235.5 cubic units

What is a Cone?

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Surface area of the cone = πr ( l + r )

where l = √ ( b² + r² )

Given data ,

Let the radius of the cone be r = 5 units

Let the height of the cone be h = 9 units

And , Volume of Cone = ( 1/3 ) πr²h

On simplifying , we get

V = ( 1/3 ) ( 3.14 ) ( 5 )² ( h )

V = 1.0467 x 25 x 9

V = 235.5 units³

Hence , the volume of cone is V = 235.5 units³

To learn more about cone click :

https://brainly.com/question/1984638

#SPJ5

The complete question is attached below :

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth.

a) 117.8 cubic units

b) 141.3 cubic units

c) 235.5 cubic units

d) 282.6 cubic units

A jar contains 12 red marbles numbered 1 to 12 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability of the given event.

Answers

blue marbles =2/3

red marbles = 6/7

The required probability to pick the blue marbles is 40%.

Given that,
A jar contains 12 red marbles numbered 1 to 12 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Number of red marbles = 12
Number of blue marbles = 8
total number of ball = 12 + 8 = 20
probability =  Number of favorable outcomes / total outcome
Probability of the picking blue marble = 8 / 20 = 0.40

Thus, the required probability to pick the blue marbles is 40%.

Learn more about probability here:

brainly.com/question/14290572

#SPJ5

Solve the system of linear equations below.

2x + y = 5
x + y = 4


I don't just want the answer can someone explain how to do this?

Answers

Answer:

[tex]x=1\\y=3[/tex]

Step-by-step explanation:

You can use the Method of Elimination:

Multiply the first  equation by -1, add both equations and then solve for the variable "x":

[tex]\left \{ {{(-1)(2x + y )= 5(-1)} \atop {x + y = 4}} \right.\\\\\left \{ {{(-2x - y = -5} \atop {x + y = 4}} \right. \\.........................\\-x=-1\\\\(-1)(-x)=(-1)(-1)\\\\x=1[/tex]

Now substitute [tex]x=1[/tex] into any of the original equations and solve for the variable "y":

[tex]x + y = 4\\1 + y = 4\\y=4-1\\y=3[/tex]

Find the distance between point A and point B. A coordinate plane is shown with point A located at left-parenthesis negative 4 comma negative 3 right-parenthesis and point B located at left-parenthesis negative 4 comma 4 right-parenthesis. A. 5 units B. 6 units C. 7 units D. 8 units

Answers

Answer: 7 units

Explanation:

We have two points, (-4,-3) and (-4,4). The X values are both the same (-4). This means we will be working with the Y values. We need to find the distance between -3 and 4. We can use inverse operations to assist us. -3 + 7 = 4. Therefore, we know the distance between these two points is 7 units.

Final answer:

The distance between point A and point B is simply the difference in their y-coordinates since they share the same x-coordinate, resulting in a distance of 7 units.

Explanation:

To find the distance between two points on a coordinate plane, you can use the distance formula. However, in this case, since points A and B have the same x-coordinate, we can calculate the distance by looking at the difference in their y-coordinates. Point A is at (-4, -3) and Point B is at (-4, 4).

The difference in the y-coordinates is 4 - (-3) = 4 + 3 = 7. Therefore, the distance between point A and point B is 7 units, which means the correct answer is C. 7 units.

Which of the following is the formula for the volume of a pyramid with base area B and height h?

A. [tex]V=\frac{1}{3} Bh[/tex]
B. [tex]V=Bh[/tex]
C. [tex]V=\frac{1}{3} Bh^2[/tex]
D.[tex]V=-\frac{1}{3} Bh[/tex]

Answers

Answer:

Correct choice is A.

Step-by-step explanation:

We have to find about which of the given choices is the formula for the volume of a pyramid with base area B and height h.

We know that formula of volume of pyramid is given by:

[tex]volume = \frac{1}{3}\left(Base\ area\right)\left(Height\right)[/tex]

Plug the given values

[tex]volume = \frac{1}{3}\left(B\right)\left(h\right)[/tex]

So the correct choice is A.

Answer: A.  [tex]\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

Step-by-step explanation:

We know that the volume of a pyramid is given by :-

[tex]\text{Volume}=\dfrac{1}{3}\times\text{Base Area of the pyramid}\times\text{Height of pyramid}[/tex]

Let B be the Base Area of the pyramid and h be the Height of pyramid, then the formula for the volume of a pyramid with base area B and height h will become :-

[tex]\text{Volume}=\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

Hence, the formula for the volume of a pyramid with base area B and height h =[tex]\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

What graph shows the solution set of the inequality x^2+10x+16/x-3 >0

Answers

[tex]x < - 10.434462 \\ x > 0[/tex]

Answer:

D

Step-by-step explanation:

The equation of a parabola is given.



y=34x2−6x+15



What are the coordinates of the vertex of the parabola?



Enter your answer in the boxes.

(
,
)

Answers

ANSWER

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

EXPLANATION

The given parabola has equation;

[tex]y = 34 {x}^{2} - 6x + 15[/tex]

Comparing this equation to

[tex]y = a{x}^{2} + bx + c[/tex]

we have

a=34, b=-6 and c=15

The x-coordinate of the vertex is given by:

[tex]x = \frac{ - b}{2a} [/tex]

[tex]x = \frac{ - - 6}{2(34)} [/tex]

[tex]x = \frac{ 6}{2(34)} [/tex]

[tex]x = \frac{ 3}{34} [/tex]

The y-coordinates of the vertex is obtained by substituting the x-value of the vertex into the equation:

[tex]y = 34( { \frac{3}{34} })^{2} - 6( \frac{3}{34}) + 15[/tex]

[tex]y = { \frac{9}{34} } - \frac{18}{34}+ 15[/tex]

[tex]y = \frac{501}{34} [/tex]

The vertex is

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

Answer: (4,3)

He meant 3/4 not 34

A teacher instituted a,new reading program at school. After 10 weeks in the program it was found that the mean reading speed of a random same 19second grade students was 94.6 wpm. What might you conclude based on this result?

Answers

The reading program really improved some of the student's reaping speeds.

The range of F(x) = logb x is the set of all real numbers. True or false

Answers

The range of F(x) = logb x is the set of all real numbers.

TRUE

The range of F(x) = logb x is the set of all real numbers since the correct option is True.

How to find a Domain?

The domain of this function is R+ or a positive real number For range if b&gt;1  function will be an increasing function and the graph will be asymptotic to the negative y-axis. which implies if x goes to infinity f(x) goes to infinity and vice versa if 0&lt;b&lt;1 function will be a decreasing and graph will be asymptotic to the positive y-axis. which implies if x goes to infinity f(x) goes to 0 and vice-versa the range of the above function is all real numbers.

Learn more about the domain here: https://brainly.com/question/13113489

#SPJ2

f(x)= 7x^5+35x^4-2x^3-4x^2+30x+8
find f(-5)

Answers

Answer:

8

Step-by-step explanation:

When you are told to find f(-5), that means that you are to sub in a -5 for every x you see.  That -5 could be any number or expression.  Subbing in a -5 looks like this:

[tex]7(-5)^5+35(-5)^4-2(-5)^3-4(-5)^2+30(-5)+8[/tex]

Be careful with all those negatives.  Doing the math on that gives you that f(-5) = 8

Write the sentence as a conditional statement. Two parallel lines lie in the same plane. If two lines are parallel, then the lines lie in the same plane. If two lines lie in the same plane, then the lines are parallel.

Answers

Answer:

The conditional statement is:

If two lines are parallel then they lie in the same plane.Step-by-step explanation:

We know that a conditional statement is the statement which is written in the form of:

        If  p then q  i.e.  p → q

where p is the hypothesis of the statement.

and q is the conclusion  of the statement which is based on the hypothesis.

Here we are given a statement as:

 Two parallel lines lie in the same plane.

i.e. the hypothesis of the conditional statement is:

Two lines are parallel.

and conclusion is: They will lie in the same plane

( Because if two lines lie in the same plane then we can't conclude that they will be parallel )

Two friends leave there houses and go towards each others, one friend runs 8 miles a hour, the other runs 7 miles an hour, there houses are 20 miles apart they both leave at 6:00 pm, what time do they meet each other?

Answers

hi there the answer is 7:30 see the picture

What are the answers and why?

Answers

Answer:

[tex]\boxed{\text{(v) and (viii)}}[/tex]

Step-by-step explanation:

The three step test for continuity states that a function ƒ(x) is continuous at a point x = a if three conditions are satisfied:

f(a) is defined. The limit of ƒ(x) as x approaches a exists. The limit of ƒ(x) as x approaches a is equal to f(a).

(i) Left-hand limit = right-hand limit.

Pass. The limit from either side is 8.

(ii) Left-hand limit = limit.  

Pass. If the limits from either direction exist, the limit exists.

(iii) Limit as x ⟶ ∞ is not part of the three-step test.

(iv) Limit as x ⟶ 1 exists. Pass.

(v)  f(1) is defined.

FAIL. f(1) is not defined.

(vi) Limit as x ⟶ ∞ is not part of the three-step test.

(vii) Passing the three-step test is not a step in the test.

(viii) The limit as x ⟶ 1 does not equal f(1).

FAIL. f(1) is undefined.

The steps in the three-step test for which the function fails are [tex]\boxed{\textbf{(v) and (viii)}}[/tex].

What number should both sides of the following equation be multiplied by in order to solve for x?

x/7.25= 4

4
7.25
7
29

Answers

Answer:

7.25

Step-by-step explanation:

Multiplying both sides of this equation by 7.25 will both eliminate the fraction and isolate (solve for) x;

7.25(x/7.25= 4) → x = 4(7.25)

                             x = 29

The answer is 29

U Multiply 7.25 and 4 and you get 29

Check your a answer by putting 29 in for x and it's correct

I hope this helped you guys

Determine if (-2,6) and (4,12) are solutions to the system of equations:

y = x + 8
2y = x2 + 8

A) Both are solutions.
B) Neither is a solution.
C) It cannot be determined
D) Only (-2,6) is a solution.

Answers

The given points (-2,6) and (4,12) are the solution of the given equations. Option A is correct.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given a system of equations,
y = x + 8  - - - - (1)

2y = x² + 8 - - - (2)

In order to determine that the points (-2,6) and (4,12) both are solutions of the given system of equations we must put the points in the equations,
So,
Put (-2, 6) in both equations,

Equation 1
put x = -2,
y = -2 + 8
y = 6

Equation 2
2y = [-2]² + 8
y = 4 + 8 / 2
y = 6

So points (-2, 6) is the solution of the given system of equation,

Similarly, by assigning the other point in the equation gives the same solutions

Thus, the given points (-2,6) and (4,12) are the solution of the given equations. Option A is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ5

Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C. If angle BDA = 20 degrees, what is the measure of angle CBD? Answer choices: a) 70 degrees b) 20 degrees c) 120 degrees d) 140 degrees e) 40 degrees

Answers

BA and BD are radii of the circle, so triangle ABD is isosceles. Then angles BDA and BAD are congruent, and the remaining (central) angle ABD has measure

[tex]m\angle ABD=(180-2\cdot20)^\circ=140^\circ[/tex]

Angles ABD and CBD are supplementary, so

[tex]m\angle CBD=(180-140)^\circ=40^\circ[/tex]

and the answer is E.

The measure of the angle CBD is 40°.

What is a circle?

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

According to the given problem,

BA and BD are radii of the circle.

Triangle ABD is isosceles.

Angles BDA and BAD are congruent.

m∠ABD = (180 - 2*20)

              = 140°

Angles ABD and CBD are supplementary, so,

∠CBD = 180 - 140

           = 40°

Hence, the measure of the angle CBD is 40°.

Learn more about circles here: https://brainly.com/question/11833983

#SPJ2

The people of Bridgetown wanted to build a bridge across a nearby river. Since they were poor swimmers, their master Trigonomos agreed to measure the width of the river without actually crossing it. Trigonomos spotted a tree across the river and marked the spot directly across from it. Then he walked to another point 15 meters down the river and found that the angle between his side of the river and the line connecting him to the tree was 76?, degree . What is the width of the river?

Answers

Answer:

60.2 m

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

Tan = Opposite/Adjacent

The width of the river is the side of a right triangle opposite the angle of 76°. The 15 m distance is the length of the side adjacent to the measured angle. So, we have ...

tan(76°) = width/(15 m)

Multiplying by 15 m, we get ...

width = (15 m)tan(76°) ≈ 60.2 m

The width of the river is about 60.2 m.

Answer:

the answer is 60.16

Step-by-step explanation:

got it right

What is the volume of the cylinder below

Answers

Answer:

D

Step-by-step explanation:

Answer:

The volume of oblique cylinder is 252π cm³

D is correct.

Step-by-step explanation:

We are given a oblique cylinder whose radius 6 and slant height 8, vertical height 7

Volume of cylinder = Base area x vertical height.

Because volume of cylinder can't be change if we change oblique to vertical cylinder.

Base area [tex]=\pi r^2[/tex]

                 [tex]=\pi \times 6^2[/tex]

                [tex]=36\pi\text{ cm}^2[/tex]

Vertical height = 7 cm

Volume of cone [tex]=36\pi \times 7[/tex]

                           [tex]=252\pi\text{ cm}^3[/tex]

Hence, The volume of oblique cylinder is 252π cm³

Sales tax in one state is 4%. What is the amount of tax on a $56.70 purchase?

a. $4.57
b. $56.74
c. $2.27
d. $22.68

Answers

1) Convert 4% to decimal = .04

2) Multiply the purchase by that decimal

.04(56.70) = $2.27

C

The amount of tax on a $56.70 purchase is $2.27

How to find the amount of tax?

A tax exists as a mandatory fee or financial charge levied by any government on a person or an organization to manage revenue for public works providing the most suitable facilities and infrastructure. The collected fund exists then utilized to fund various public expenditure programs.

Sales tax in state = 4%

The amount tax on $1 purchase = $ [tex]\frac{4}{100}[/tex]  =  $ 0.04

The amount tax on a $56.70 purchase

= 56.70 * 0.04

= $2.27

Therefore option  c. $2.27 is the correct answer

To learn more about sales tax amount calculation, refer :

https://brainly.com/question/3353361
#SPJ2

Which number sentence can be used to determine n, the 9th number in the pattern

Answers

Answer would be D
Because the pattern is going by 3s and it is asking for the 9th so u just multiply 9 by 3 which give you 27 and if you want to check you answer then subtract 6 by 3 gives you 3 and theater number in the pattern is 15 so you just add 15 by 3 which is 18 and repeat the same thing until you get to the 9th number
18, 21, 24, 27...

HELLPPPPPPPPPPPPPPPPPP PLEASE WILL GIVE MORE THAN 5 POINTSSSSSSSS

In this triangle, which of the following is true?

**APEX**

| Multiple Choice |

Answers

The answer to the question is D

Answer:

The measure of x is 35 and a = 8.19

Step-by-step explanation:

What are the characteristics of the graph of the inequality x < 5?

It will use an open circle.
The ray will move to the right.
It will use a closed circle.
The ray will move to the left.

You can pick more than one.

Answers

Answer:

see explanation

Step-by-step explanation:

Given x < 5

The graph will have an open circle at 5 indicating that x is not equal to 5, which would be a closed circle.

The ray will move to the left since values less than 5 are to the left of 5

The characteristics of the graph of the inequality x < 5 tells that value of x is less then the 5. It will use an open circle and the ray will move to the left.

What are the characteristics of the graph of the inequality?

Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.

Characteristics of the graph of the inequality-

Open circle- When the value of variable is equal the given number, then the graph of the inequality has a open circle.Closed circle-When the value of variable is not equal the given number, then the graph of the inequality has a closed circle.The ray will move to the right- When the, value of variable is greater then the number, then the ray will move to the right. The ray will move to the left- When the value of variable is less then the number, then the  the ray will move to the left.

Given information-

The inequality equation given in the problem is,

[tex]x<5[/tex]

This equation represent that the value of variable x is less then the number 5.

As in the graph, the value of variable is not equal the given number. Thus the graph of the inequality x<5 has a closed circle.As in the equation, the value of variable x is less then the number 5. Thus the ray will move to the left.

Hence, the characteristics of the graph of the inequality x < 5 tells that value of x is less then the 5. It will use an open circle and the ray will move to the left.

Learn more about the characteristics of the graph of the inequality here;

https://brainly.com/question/62792

A pitcher contains 4.32-pint of lemon syrup. 12.6 pint of water are added to the syrup to make lemonade. How much lemonade is made

Answers

Answer:

16.92 pints of lemonade was made

Step-by-step explanation:

Use the divergence theorem to find the outward flux of the vector field F(xyz)= 4x^2 i + 4y^2 j + 3z^2 k across the boundary of the rectangular prism: 0

Answers

[tex]\vec F(x,y,z)=4x^2\,\vec\imath+4y^2\,\vec\jmath+3z^2\,\vec k\implies\nabla\cdot\vec F=8x+8y+6z[/tex]

Let [tex]S[/tex] be the surface of the rectangular prism bounded by the planes [tex]x=0[/tex], [tex]x=a[/tex], [tex]y=0[/tex], [tex]y=b[/tex], [tex]z=0[/tex], and [tex]z=c[/tex]. By the divergence theorem, the integral of [tex]\vec F[/tex] over [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over the interior of [tex]S[/tex] (call it [tex]R[/tex]):

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]

[tex]=\displaystyle\int_0^c\int_0^b\int_0^a(8x+8y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{abc(4a+4b+3c)}[/tex]

Answer:

[tex]\displaystyle \iiint_D {\nabla \cdot \textbf{F}} \, dV = \boxed{6875}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Multivariable Calculus

Partial Derivatives

Vector Calculus (Line Integrals)

Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]

Div and Curl:

[tex]\displaystyle \text{div \bf{F}} = \nabla \cdot \textbf{F}[/tex][tex]\displaystyle \text{curl \bf{F}} = \nabla \times \textbf{F}[/tex]

Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]

Step-by-step explanation:

*Note:
Your question is incomplete, but I have defined the missing portions of the question below.

Step 1: Define

Identify given.

[tex]\displaystyle \textbf{F} (x, y, z) = 4x^2 \hat{\i} + 4y^2 \hat{\j} + 3z^2 \hat{\text{k}}[/tex]

[tex]\displaystyle \text{Region (Boundary de} \text{fined by rectangular prism):} \left\{ \begin{array}{ccc} 0 \leq x \leq 5 \\ 0 \leq y \leq 5 \\ 0 \leq z \leq 5 \end{array}[/tex]

Step 2: Find Flux Pt. 1

[Vector Field] Find div F:
[tex]\displaystyle \text{div } \textbf{F} = \frac{\partial}{\partial x}4x^2 + \frac{\partial}{\partial y}4y^2 + \frac{\partial}{\partial z}3z^2[/tex][div F] Differentiate [Partial Derivatives and Basic Differentiation Techniques]:
[tex]\displaystyle \text{div } \textbf{F} = 8x + 8y + 6z[/tex]

Step 3: Find Flux Pt. 2

[Flux] Define:
[tex]\displaystyle \Phi = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex][Divergence Theorem] Substitute in div F:
[tex]\displaystyle \Phi = \iiint_D {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz[/tex][Flux] Substitute in region D:
[tex]\displaystyle \Phi = \int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz[/tex]

We can evaluate the Flux integral (Divergence Theorem integral) using basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 \int\limits^5_0 {4x^2 + x \big( 8y + 6z \big) \bigg| \limits^{x = 5}_{x = 0}} \, dy \, dz \\& = \int\limits^5_0 \int\limits^5_0 {\big( 40y + 30z + 100 \big)} \, dy \, dz \\& = \int\limits^5_0 {20y^2 + y \big( 30z + 100 \big) \bigg| \limits^{y = 5}_{y = 0}} \, dz \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 {\big( 150z + 1000 \big)} \, dz \\& = \big( 75z^2 + 1000z \big) \bigg| \limits^{z = 5}_{z = 0} \\& = \boxed{6875} \\\end{aligned}[/tex]

∴  [tex]\displaystyle \Phi = \boxed{6875}[/tex]

---

Learn more about Divergence Theorem: https://brainly.com/question/2407209

Learn more about multivariable calculus: https://brainly.com/question/7964566

---

Topic: Multivariable Calculus

Unit: Stokes' Theorem and Divergence Theorem

Which graph represents the function f(x) = 1/x - 1?

Answers

Answer:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x) = 1/x - 1

Domain

All real numbers except for {0}

Answer:

It would be the fourth graph, D

Explanation:

When faced with these problems, you can either plot it on your own or you can use a graph generator online.

mary took a trip to orlando that took 3 hours long. mary forgot to check the time as she left, but when she got to orlando, her phone read 10:00 am. what time did mary start her trip?

Answers

Where was Mary leaving from to get to Orlando? : )

because it's still in the morning so e you can easily subtract 3 hours from

10:00 am.

10 - 3 = 7:00 am

Other Questions
Simplify 2x - 8x - 6y + 9 -14 + x + 11y. A)5x - 5y - 5 B)-5x + 5y - 5 C)5x + 5y + 5 D)-5x - 5y + 5 Which two continents are the most densely populated?a]South America and Europeb]North America and Asiac]Australia and Europed]Africa and Asia Amber and Austin were driving the same route from college to their home town. Amber left 2 hours before Austin. Amber drove at an average speed of 55 mph, and Austin averaged 75 mph per hour. After how many hours did Austin catch up with Amber? What is the magnitude and phase of X.[tex]X=\sqrt{3-4i}[/tex] What is the measure of the missing angle? need helpppppppppp pleaseeeeeeeeeeeeeeeeeeeeeeeeeee In the straightedge and compass construction of the equilateral triangle below, which of the following reasons can you use to prove that AC BC? How is the idea of a social contract reflected in the Declaration of Independence John is a 70-year-old man. His doctor determined that John has a type of progressive dementia. Which eponym most likely describes his condition?A. Addison diseaseB. Prkinson diseaseC. Pager diseaseD. Alzheimer disease Consider the status of the black-footed ferret. What is the MOST logical contributing factor to its endangered status? A) The exponential growth of ferret predator populations. B) Human encroachment that has greatly reduced the prairie dog populations. C) The growing habitat range of the prairie dog populations throughout the United States. D) Climatic change that has significantly modified the climate of the central United States. Help please! 20 points!(VIEW THE PICTURE)Please explain how you got your answerWhat is the surface area of the paperweight?Enter your answer in the box. Graph Y is less than 1/3 X +1/2 Which is a scientific claim Drag each tile to the correct location.In which countries was Islam established through trade, and in which countries was Islam established by invading Islamic armies?PersiaIndonesiaChinaAfghanistanMalaysiaIndiatrade;invading armies; A metalworker has a metal alloy that is 25% copper and another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 50 kg of a 61% copper alloy? The metalworker should use nothing kilograms of the metal alloy that is 25% copper and nothing kilograms of the metal alloy that is 70% copper For 180 A circle has a diameter with endpoints of (-1, 5) and (5, 3). What is the center of the circle?(2, 4)(4, 4)(2, 5)(5, 1) What is the simplified form of (4j^2+6)+(2j^2-3) ?1. 6j^2-32. 6j^2+33. 6j^2+94. 4j^4+3 what is one water conservation policy in California The graph of f(x) = is shown with g(x). Which equation represents the graph of g(x)? g(x) = g(x) = g(x) = + 1 g(x) = 1